Polynomials
Add.
(11x3 – x2 + 2) + (4x3 – 5x2 – 19x – 19)
15x3 – 6x2 – 19x – 17
Factor and solve.
y = 4x2 + 16x
x = 0
x = –4
Factor and solve.
y = 25x2 – 100
x = 2
x = –2Factor and solve.
y = x2 + 3x – 10
x = –5
x = 2
Use the quadratic formula and solve.
x2 – 5x – 14 = 0
x = –2
x = 7
Subtract.
(2x2 – 14x + 8) – (–15x2 – 13x + 2)
17x2 – 1x + 6
Factor and solve.
y = 2x2 – 10x
x = 0
x = 5
Factor and solve.
y = 36x2 – 144
x = 2
x = –2
Factor and solve.
y = x2 – x – 6
x = –2
x = 3
Use the quadratic formula and solve.
x2 – 4x + 4 = 0
x = 2
Multiply.
(–3x2 + –9x + 4)(2x + 10)
–6x3 – 48x2 – 82x + 40
Factor and solve.
y = –8x2 – 8x
x = 0
x = –1
Factor and solve.
y = 9x2 – 225
x = 5
x = –5
Factor and solve.
y = 2x2 + 43x + 21
x = –21
x = –1/2 or –0.5
Use the quadratic formula and solve.
2x2 + 2x – 12 = 0
x = 2
x = –3
Multiply.
(4x – 2)(5x + 3)(6x – 1)
120x3 – 8x2 – 38x + 6
Factor and solve.
y = –6x2 – 45x
x = 0
x = –15/2 or –7.5
Factor and solve.
y = 49x2 – 81
x = 9/7
x = –9/7
Factor and solve.
y = 4x2 – 20x + 24
x = 2
x = 3
Use the quadratic formula and solve.
2x2 + 9x = –7
x = –1
x = –7/2 or –3.5
Multiply.
(–x3 – 11x2 + 5x – 7)(4x2 – 6x – 12)
–4x5 – 38x4 + 98x3 + 74x2 – 18x + 84
The solutions are x = 0 and x = –7/3. What was the original equation?
y = __x2 + __x
y = 3x2 + 7x
OR
y = x2 + 7/3x
Write a quadratic that is a difference of perfect squares with solutions of x = 8/5 and x = –8/5.
y = 25x2 – 64
OR
y = x2 – 64/25
A quadratic equation has two solutions:
x = –5 and x = ?
The equation is x2 + 12x + c. What is c?
c = 35
A ball is thrown off of a building. Its height (h) after t seconds is represented by the equation:
h = –4.9t2 + 12t + 20
How many seconds does it take for the ball to hit the ground?
–12 + √536
–9.8